Question

which ordered pairs represent points on the graph of this equation? select all that apply.
$y = \frac{1}{3}x$
$(-6, -2)$ $(3, 1)$
$(6, 2)$ $(-6, 5)$
$(-3, -1)$ $(0, 0)$

Explanation:

Step1: Check (-6, -2)

Substitute \( x = -6 \) into \( y = \frac{1}{3}x \). \( y = \frac{1}{3} \times (-6) = -2 \). So (-6, -2) is on the graph.

Step2: Check (3, 1)

Substitute \( x = 3 \) into \( y = \frac{1}{3}x \). \( y = \frac{1}{3} \times 3 = 1 \). So (3, 1) is on the graph.

Step3: Check (6, 2)

Substitute \( x = 6 \) into \( y = \frac{1}{3}x \). \( y = \frac{1}{3} \times 6 = 2 \). So (6, 2) is on the graph.

Step4: Check (-6, 5)

Substitute \( x = -6 \) into \( y = \frac{1}{3}x \). \( y = \frac{1}{3} \times (-6) = -2
eq 5 \). So (-6, 5) is not on the graph.

Step5: Check (-3, -1)

Substitute \( x = -3 \) into \( y = \frac{1}{3}x \). \( y = \frac{1}{3} \times (-3) = -1 \). So (-3, -1) is on the graph.

Step6: Check (0, 0)

Substitute \( x = 0 \) into \( y = \frac{1}{3}x \). \( y = \frac{1}{3} \times 0 = 0 \). So (0, 0) is on the graph.

Answer:

The ordered pairs that represent points on the graph of \( y = \frac{1}{3}x \) are \((-6, -2)\), \((3, 1)\), \((6, 2)\), \((-3, -1)\), and \((0, 0)\). The ordered pair \((-6, 5)\) is not on the graph.